Question

$66c{m}^3$ of silver is drawn into a wire $1mm$ in diameter. The length of the wire will be

(a) $78m$

(b) $84m$

(c) $96m$

(d) $108m$

Answer 1

The correct option is (b): $84m$

Given: Volume of silver $=66c{m}^3$

Diameter of wire, $d=1mm=\frac{1}{10}cm$

$\therefore$ Radius of the wire, $r=\frac{1}{10}÷2=\frac{1}{20}cm$

Let length of the drawn wire be ${}^{\prime }{l}^{\prime }cm.$

Volume of the drawn wire $=$ Volume of the given silver

$\pi r^{2}l=66$ [$\because$ Volume of wire $=$ Volume of cylinder $=\pi r^{2}h$ ]

$\Rightarrow \frac{22}{7}\times (\frac{1}{20}{)}^2\times l=66$

$\Rightarrow l=\frac{66\times 20\times 20\times 7}{22}$

$\Rightarrow l=8400cm=84m$ [$\because 100cm=1m$]